On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces

On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces

We generalize the Bogomolov-Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne-Mumford surfaces. We work over positive characteristic \(p>0\) and generalize Langer's method to smooth Deligne-Mumford stacks. As applications we obtain the Bogomo...

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Veröffentlicht in:arXiv.org 2021-04
Hauptverfasser: Jiang, Yunfeng, Kundu, Promit, Sun, Hao Max
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Inequality
Sheaves
Stacks
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description We generalize the Bogomolov-Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne-Mumford surfaces. We work over positive characteristic \(p>0\) and generalize Langer's method to smooth Deligne-Mumford stacks. As applications we obtain the Bogomolov inequality for semistable coherent sheaves on a Deligne-Mumford surface in characteristic zero, and the Bogomolov inequality for semistable sheaves on a root stack over a smooth surface which is equivalent to the Bogomolov inequality for the rational parabolic sheaves on a smooth surface \(S\). In a joint appendix with Hao Max Sun, we generalize the Bogomolov inequality formula to Simpson Higgs sheaves on tame Deligne-Mumford stacks.
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Sheaves
Stacks
title On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces
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